Home
Class 12
MATHS
If the sides of a triangle are in A.P., ...

If the sides of a triangle are in A.P., and its greatest angle exceeds the least angle by `alpha`, show that the sides are in the ration `1+x :1:1-x`, , where `x = sqrt((1- cos alpha)/(7 - cos alpha))`

Text Solution

Verified by Experts

The correct Answer is:
Thus, the sides are in the ratio `1+x :1:1:1-x.`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 2|19 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

The sides of a triangle are in A.P and the greatest angle exceeds the least by 90^(0) .The sides are in the ratio

If the sides of a triangle are in A.P. and the greatest angle of the triangle exceeds the least by 90^(@) , then sine of the third angle is

The sides of triangle are in A.P. and the greatet and least angle are theta and phi: prove that 4(1-cos theta)(1-cos phi)=cos theta+cos phi

(1)/(cos alpha+cos x)

int(1+cos alpha cos x)/(cos alpha+cos x)dx

If the sides of a triangle are in A.P and difference between the greatest and least angles is (pi)/(2) , and sin((B)/(2))=(1)/(a sqrt(b)) , then a+b = ?

The sides of a triangle are x^(2)+x+1,2x+1, and x^(2)-1. Prove that the greatest angle is 120^(@) .

(1)/(1+cos alpha.cos x)

The sides of a triangle are in AP. If the angles A and C are the greatest and smallest angle respectively, then 4 (1- cos A) (1-cos C) is equal to

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the sides of a triangle are in A.P., and its greatest angle exceeds...

    Text Solution

    |

  2. In a triangle XYZ, let x, y, z be the lengths of sides opposite to the...

    Text Solution

    |

  3. In a triangle the sum of two sides is x and the product of the same is...

    Text Solution

    |

  4. Consider a triangle A B C and let a , ba n dc denote the lengths of th...

    Text Solution

    |

  5. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

    Text Solution

    |

  6. Let PQR be a triangle of area Delta with a = 2, b = 7/2 and c =5/2, wh...

    Text Solution

    |

  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |

  8. Let A B C be a triangle such that /A C B=pi/6 and let a , ba n dc deno...

    Text Solution

    |

  9. a triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  11. A straight line through the vertex P of a triangle PQR intersects the ...

    Text Solution

    |

  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  16. Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...

    Text Solution

    |

  17. In Delta ABC, which one is true among the following ?

    Text Solution

    |

  18. Let a vertical tower A b have its end A on the level ground. Let C be ...

    Text Solution

    |

  19. ABCD is a trapezium such that AB and CD are parallel and BC | CD. If ...

    Text Solution

    |

  20. For a regular polygon, let r and R be the radii of the inscribed and ...

    Text Solution

    |

  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |